Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the m...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210182 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras / S. Fujiwara, Y. Gyoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732413604462592 |
|---|---|
| author | Fujiwara, S. Gyoda, Y. |
| author_facet | Fujiwara, S. Gyoda, Y. |
| citation_txt | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras / S. Fujiwara, Y. Gyoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the maximal degree matrices of the F-polynomials called the F-matrices and show that the F-matrices have self-duality, which is analogous to the duality between the C- and G-matrices.
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| first_indexed | 2025-12-07T21:24:39Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210182 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:39Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fujiwara, S. Gyoda, Y. 2025-12-03T14:28:20Z 2019 Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras / S. Fujiwara, Y. Gyoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 13F60 arXiv: 1808.02156 https://nasplib.isofts.kiev.ua/handle/123456789/210182 https://doi.org/10.3842/SIGMA.2019.040 We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the maximal degree matrices of the F-polynomials called the F-matrices and show that the F-matrices have self-duality, which is analogous to the duality between the C- and G-matrices. The authors are grateful to Professor Tomoki Nakanishi for useful comments and advice. We also thank Toshiya Yurikusa for insightful comments about the principal extension. We would also like to express our gratitude to the referees. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras Article published earlier |
| spellingShingle | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras Fujiwara, S. Gyoda, Y. |
| title | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras |
| title_full | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras |
| title_fullStr | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras |
| title_full_unstemmed | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras |
| title_short | Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras |
| title_sort | duality between final-seed and initial-seed mutations in cluster algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210182 |
| work_keys_str_mv | AT fujiwaras dualitybetweenfinalseedandinitialseedmutationsinclusteralgebras AT gyoday dualitybetweenfinalseedandinitialseedmutationsinclusteralgebras |